A similar question has already been settled in Delaware: Edward Kaufman, a longtime aide to Sen. Joseph Biden, will take his Senate seat after Mr. Biden assumes the vice presidency. But speculation about the Illinois pick has run rampant. Gov. Rod Blagojevich (D) has promised to name someone before the end of the year. [Editor's note: The original version misidentified Sen. Biden's state.]

Opinions differ sharply on key questions: Does the replacement need to be an African-American to ensure that the Senate will continue to have at least one black member? Should it be a “placeholder” who doesn’t plan to run in 2010, or someone who has a good shot at winning a statewide election in two years? Will Governor Blagojevich seek to help his own dim chances at reelection by naming one of his political rivals?

With the governor’s approval rating currently hovering at about 13 percent, the decision gives him a rare chance for a positive moment in the spotlight. But some observers caution that any choice he makes is likely to make numerous groups unhappy.

“In normal times, [Blagojevich] would pick somebody who can help him in a 2010 primary, but there isn’t anyone out there who can help him with what he needs,” says Paul Green, a political scientist at Roosevelt University in Chicago. “It’s a multiple-choice test with no right answer.... If he resurrected Mother Teresa, they’d say it’s a bad choice because she lacks experience.” Anyone he picks, adds Professor Green, will be compared with his predecessor, and “whomever he picks will not be Obama.”

Representative Jackson has made it clear he’d like the job, commissioning and circulating a Zogby poll that revealed him as the favorite among 10 possible candidates and that showed him having a good chance at being reelected in two years.

Speculation that the governor could try to help himself by removing a potential primary rival, such as Attorney General Madigan, is interesting, says Professor Redfield. But in the end, “he only has one appointment and way too many people who want to run against him.”

Others suggest he might opt not to give any candidate a leg up in the 2010 race and thus go with a relatively safe “placeholder” choice, like state Senator Jones, also an African-American and a politician with whom Blagojevich has a close relationship. But some also note that the governor has a reputation for liking to surprise pundits and to make a splash.

An African-American is the most likely pick, Professor Simpson agrees. He hopes the governor will tap someone who, like Jackson, has more national experience and may be able to do more for the state.

One wild-card option: US Attorney Patrick Fitzgerald, the prosecutor behind many of the corruption investigations into the Blagojevich administration. That choice not only could prove to be popular with the public, but would also remove a big thorn from the governor’s side.

Mr. Fitzgerald “would make a lot of people feel really happy,” says Green.